Question

If the sun's angle of elevation increases from ${30}^{\circ }$ to ${60}^{\circ }$, length of shadow of a post ___ .

Answer 1

Let the length of the post be x

Angle of elevation = $\theta ={30}^{\circ }$
$\Rightarrow tan\theta =\frac{AB}{BC}$
$\Rightarrow tan\theta =\frac{x}{BC}$
$\Rightarrow tan{30}^{\circ }=\frac{1}{\sqrt{3}}$
$\Rightarrow \frac{x}{BC}=\frac{1}{\sqrt{3}}$
Therefore, BC = $x\sqrt{3}$

angle of elevation = ${60}^{\circ }$

$\Rightarrow tan\theta =\frac{AB}{BC}$
$\Rightarrow tan\theta =\frac{x}{BC}$
$\Rightarrow tan{60}^{\circ }=\frac{1}{\sqrt{3}}$
$\Rightarrow \frac{x}{BC}=\sqrt{3}$
Therefore, BC = $\frac{x}{\sqrt{3}}$